express the following as a rational number raised to a positive exponent
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Express as a power of a rational number with positive exponent: [(45)−2]4
. If the answer is (54)m
, find the value of m
.
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Hint: Here, we need to express the given expression as a rational number with positive exponent, and find the value of m
. We will use the rules of exponents to simplify the given expression to a rational number with a positive exponent. Then, we will equate it to (54)m
, and compare them to find the value of m
.
Formula Used: We will use the rules of exponents:
If a number raised to an exponent is again raised to an exponent, the new power is the product of the exponents. This can be written as (ab)c=ab×c
.
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