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QuestionEvaluate ((14)7(14)6)2\left(\frac{\left(\frac{1}{4}\right)^{7}}{\left(\frac{1}{4}\right)^{6}}\right)^{2}. Options: 1, 1 \frac{1}{16}, 116\frac{1}{16}, 132\frac{1}{32}.

Studdy Solution

STEP 1

Assumptions1. We are using the laws of exponents. . The base for both the numerator and the denominator is 14\frac{1}{4}.
3. The exponent for the numerator is7 and for the denominator is6.
4. The entire expression is squared.

STEP 2

First, we need to simplify the expression inside the parentheses. According to the laws of exponents, when we divide two exponents with the same base, we subtract the exponent of the denominator from the exponent of the numerator.
((14)7(14)6)=(14)7−6\left(\frac{\left(\frac{1}{4}\right)^{7}}{\left(\frac{1}{4}\right)^{6}}\right) = \left(\frac{1}{4}\right)^{7-6}

STEP 3

Now, subtract the exponents to simplify the expression.
(1)7−6=(1)1\left(\frac{1}{}\right)^{7-6} = \left(\frac{1}{}\right)^{1}

STEP 4

implify the expression further.
(14)1=14\left(\frac{1}{4}\right)^{1} = \frac{1}{4}

STEP 5

Now, we need to square the result according to the original problem.
(14)2\left(\frac{1}{4}\right)^{2}

STEP 6

Calculate the final result.
(14)2=116\left(\frac{1}{4}\right)^{2} = \frac{1}{16}The answer is 116\frac{1}{16}.

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