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Page 1 Base and Exponent Drill Directions: Answer the following questions in the spaces provided and write the coefficient, base, and exponent for each answer. No calculators allowed! 3b x 4b x 6b x 8 2. 2c x 4c x 5 x 6 3. 9d x 4d x 2d x 5d 4. 5. 6e x 3e x 2 x 7 1. 2a x 2a x 2a x 2 Coefficient: ____________ Base: ____________ Exponent: ____________ f x 2f x 3f x 4f x 5f 6. Coefficient: ____________ Base: ____________ Exponent: ____________ Coefficient: ____________ Base: ____________ Exponent: ____________ 3g x 3g x 3g x3g 7. Coefficient: ____________ Base: ____________ Exponent: ____________ Coefficient: ____________ Base: ____________ Exponent: ____________ Coefficient: ____________ Base: ____________ Exponent: ____________ 4h x 5h x 6h x 7h x 8 8. Coefficient: ____________ Base: ____________ Exponent: ____________ 2j x 3j x 5j x 8j x 4j 9. Coefficient: ____________ Base: ____________ Exponent: ____________ Coefficient: ____________ Base: ____________ Exponent: ____________ 6k x 5k x 3k x 2k x 4k x 3k 10. Coefficient: ____________ Base: ____________ Exponent: ____________ Page 2 Base and Exponent Drill Directions: Answer the following questions in the spaces provided and write the coefficient, base, and exponent for each answer. No calculators allowed! 3b x 4b x 6b x 8 2. 2c x 4c x 5 x 6 3. 9d x 4d x 2d x 5d 4. 5. 6e x 3e x 2 x 7 1. 2a x 2a x 2a x 2 Coefficient: ____________ Base: ____________ Exponent: ____________ f x 2f x 3f x 4f x 5f 6. Coefficient: ____________ Base: ____________ Exponent: ____________ Coefficient: ____________ Base: ____________ Exponent: ____________ 3g x 3g x 3g x3g 7. Coefficient: ____________ Base: ____________ Exponent: ____________ Coefficient: ____________ Base: ____________ Exponent: ____________ Coefficient: ____________ Base: ____________ Exponent: ____________ 4h x 5h x 6h x 7h x 8 8. Coefficient: ____________ Base: ____________ Exponent: ____________ 2j x 3j x 5j x 8j x 4j 9. Coefficient: ____________ Base: ____________ Exponent: ____________ Coefficient: ____________ Base: ____________ Exponent: ____________ 6k x 5k x 3k x 2k x 4k x 3k 10. Coefficient: ____________ Base: ____________ Exponent: ____________ Base and Exponent Drill ANSWER KEY 3b x 4b x 6b x 8 2. 2c x 4c x 5 x 6 3. 9d x 4d x 2d x 5d 4. 5. 6e x 3e x 2 x 7 1. 2a x 2a x 2a x 2 Coefficient: ____16____ Base: ___a______ Exponent: ____3_____ f x 2f x 3f x 4f x 5f 6. Coefficient: ___120____ Base: ___f______ Exponent: ____5_____ Coefficient: ___576___ Base: ____b_____ Exponent: __3_______ 3g x 3g x 3g x3g 7. Coefficient: ___81_____ Base: ____g_____ Exponent: ____4____ Coefficient: __240___ Base: ___c______ Exponent: __2_______ Coefficient: ___360___ Base: ___d______ Exponent: ___4______ 4h x 5h x 6h x 7h x 8 8. Coefficient: __6720___ Base: ___h______ Exponent: ___4______ 2j x 3j x 5j x 8j x 4j 9. Coefficient: __960____ Base: __j_______ Exponent: ___5______ Coefficient: __252_____ Base: __e_______ Exponent: ___2______ 6k x 5k x 3k x 2k x 4k x 3k 10. Coefficient: __2160___ Base: ____k_____ Exponent: ___6______Read More
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FAQs on Visual Worksheet: Base and Exponent - Mathematics Class 8- New NCERT (Ganita Prakash)
| 1. What is the definition of a base and an exponent in mathematics? |  |
Ans. In mathematics, a base is the number that is being multiplied, while an exponent indicates how many times the base is multiplied by itself. For example, in the expression 2³, 2 is the base and 3 is the exponent, which means 2 is multiplied by itself 3 times (2 × 2 × 2).
| 2. How do you simplify expressions involving exponents? | |
Ans. To simplify expressions with exponents, you can use the laws of exponents. Some key rules include:
1. aᵐ × aⁿ = aᵐ⁺ⁿ (multiply the bases and add the exponents),
2. aᵐ ÷ aⁿ = aᵐ⁻ⁿ (divide the bases and subtract the exponents),
3. (aᵐ)ⁿ = aᵐⁿ (multiply the exponents).
By applying these rules, you can reduce complex exponent expressions to simpler forms.
| 3. What are some real-life applications of exponents? | |
Ans. Exponents are widely used in various real-life applications, such as in finance for calculating compound interest, in science for dealing with large numbers like population sizes or distances in space (using scientific notation), and in computer science for analyzing algorithms and data storage (e.g., binary systems). Understanding exponents helps in interpreting exponential growth and decay in different contexts.
| 4. Can you explain the concept of negative exponents? | |
Ans. Negative exponents represent the reciprocal of the base raised to the opposite positive exponent. For example, a⁻ⁿ = 1/aⁿ. This means if you have 2⁻², it can be expressed as 1/2², which equals 1/4. Negative exponents are useful in simplifying fractions and expressing very small numbers.
| 5. What is the difference between integer exponents and fractional exponents? | |
Ans. Integer exponents indicate repeated multiplication of a base, such as a² = a × a. Fractional exponents, on the other hand, represent roots. For example, a^(1/n) corresponds to the n-th root of a, meaning a^(1/2) is the square root of a. Thus, a^(m/n) can be interpreted as the n-th root of a raised to the m-th power, combining both concepts.
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