15 Questions MCQ Test General Test Preparation for CUET - Test: Exponents- 3
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Simplify the following expression without a calculator:
Detailed Solution for Test: Exponents- 3 - Question 4
The easiest way to simplify is to work from the inside out. We should first get rid of the negatives in the exponents. Remember that variables with negative exponents are equal to the inverse of the expression with the opposite sign. For example
So using this, we simplify:
Now when we multiply variables with exponents, to combine them, we add the exponents together. For example, (a2)(a2)=a2+2=a4 Doing this to our expression we get it simplified to
The next step is taking the inside expression and exponentiating it. When taking an exponent of a variable with an exponent, we actually multiply the exponents. For example, (a2)4=a(2∗4)=a8.
The other rule we must know that is an exponent of one half is the same as taking the square root. So for the So using these rules,
Detailed Solution for Test: Exponents- 3 - Question 5
First, write each expression as a base 3 logarithm:
3=log327 since 33=27
Rewrite the expression accordingly, and apply the logarithm sum and difference rules:
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