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Exponents Formulas
There are various laws of exponents that you should practice and remember in order to thoroughly understand the exponential concepts. The following exponent law is detailed with examples on exponential powers and radicals and roots.
Properties of Exponents and Radicals
Example1: If m2+n2+o2 = mn+no+om, simplify [ym/yn]m-n × [yn/yo]n-o × [yo/ym]o-m
Sol:
Using ma/nb = ma-b, we obtain
→ (ym-n)m-n×(yn-o)n-o×(yo-m)o-m
Using the formula
(m-n)2 = m2+n2-2mn in the exponent,
→y(m²+n²−2mn) * y(m²+o²−2no) * y(o²+m²−2om)
Doing the Math
ma.mb=ma+b
→ y(m²+n²−2mn+n²+o²−2no+o²+m²−2om)
→ y2(m²+n²+o²−(mn+no+om))
→ y2(0)2(0)
→ y0=1
Example 2: Find y if 32y-1+32y+1=270
Sol: We will first take out a term in common, with which we obtain
→ 32y-1(1+32)
See that here, we are using the formula for any non-integer am+n = am. an in expressing 32y+1 as a product of 32y-1 and 32.
32y-1(10)=270
32y-1=27
32y-1=33
2y−1=3
y = 2.
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FAQs on Important Formulas: Exponents - Quantitative for GMAT
| 1. What is the formula for finding the value of an exponent? |  |
Ans. The formula for finding the value of an exponent is expressed as a^b, where 'a' is the base and 'b' is the exponent. This means that the base 'a' is multiplied by itself 'b' times.
| 2. How do you simplify an exponential expression? | |
Ans. To simplify an exponential expression, you can use the following rules:
- When multiplying powers with the same base, add their exponents: a^m * a^n = a^(m + n).
- When dividing powers with the same base, subtract their exponents: a^m / a^n = a^(m - n).
- When raising a power to another power, multiply the exponents: (a^m)^n = a^(m * n).
| 3. What is the power of a power rule in exponents? | |
Ans. The power of a power rule states that when raising a power to another power, you multiply the exponents. This rule is expressed as (a^m)^n = a^(m * n). For example, (2^3)^2 = 2^(3 * 2) = 2^6 = 64.
| 4. How do you simplify expressions with negative exponents? | |
Ans. To simplify expressions with negative exponents, you can use the following rule: a^(-n) = 1 / a^n. This means that any term with a negative exponent can be rewritten as its reciprocal with a positive exponent. For example, 2^(-3) = 1 / 2^3 = 1 / 8.
| 5. How do you simplify expressions with zero exponents? | |
Ans. When an exponent is zero, the simplified value of the expression is always 1. This means that any base raised to the power of zero equals 1. For example, 5^0 = 1.
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