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QuestionChoose the equivalent expression for (−3)4(−3)2\frac{(-3)^{4}}{(-3)^{2}}: 1) (−3)2(−3)4\frac{(-3)^{2}}{(-3)^{4}} 2) (−3)6(−3)4\frac{(-3)^{6}}{(-3)^{4}} 3) (−3)(−3)5\frac{(-3)}{(-3)^{5}} 4) (−3)5(−3)\frac{(-3)^{5}}{(-3)}

Studdy Solution

STEP 1

Assumptions1. The base of the exponent is -3. The exponents are whole numbers3. We are using the laws of exponents to simplify the expression

STEP 2

We are given the expression (−)4(−)2\frac{(-)^{4}}{(-)^{2}}. According to the laws of exponents, when we divide two exponents with the same base, we subtract the exponent in the denominator from the exponent in the numerator.
aman=am−n\frac{a^{m}}{a^{n}} = a^{m-n}

STEP 3

Now, plug in the given values for the base and exponents to simplify the expression.
(−3)(−3)2=(−3)−2\frac{(-3)^{}}{(-3)^{2}} = (-3)^{-2}

STEP 4

Subtract the exponents.
(−3)4−2=(−3)2(-3)^{4-2} = (-3)^{2}

STEP 5

Calculate the value of (−3)2(-3)^{2}.
(−3)2=9(-3)^{2} =9So, the expression (−3)4(−3)2\frac{(-3)^{4}}{(-3)^{2}} is equivalent to9.
Looking at the given options, none of them is equivalent to9. Therefore, there seems to be a mistake in the problem as none of the options match the solution.

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