Question

Blake simplified the expression (startfraction x superscript 12 baseline over x superscript negative 3 baseline endfraction) superscript 5 to startfraction 1 over x superscript 20 baseline endfraction. What was blake’s mistake? he added 5 to the exponent in the numerator instead of multiplying. He subtracted the exponents in the parentheses instead of dividing. He multiplied only the exponent in the numerator of the fraction by 5. He divided the exponents in the parentheses instead of subtracting.

Answer 1

Blake's mistake is (d) He divided the exponents in the parentheses instead of subtracting.

How to determine the mistake

The expression is given as:

$(\frac{x^{12}}{x^{-3}})^5 = \frac{1}{x^{-20}}$

The actual solution is as follows:

$(\frac{x^{12}}{x^{-3}})^5 = (x^{12+3})^5$

Add the exponents

$(\frac{x^{12}}{x^{-3}})^5 = (x^{15})^5$

Multiply 15 by 5

$(\frac{x^{12}}{x^{-3}})^5 = x^{75}$

Blake's simplified expression showed that:

He divided 12 by -3 and then multiplied the result by 5

Hence, Blake's mistake is (d) He divided the exponents in the parentheses instead of subtracting.

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