Question

Lauren simplified the expression

as shown

(m-) = m+7+(-5) = m+12 - 1

m12

Which statement explains Lauren's error?

Answer 1

Correct Question

Lauren simplified the expression $(m^{-7} )^{-5}$

as shown

$(m^{-7} )^{-5} = m^{-7+(-5)} = m^{-12} = \frac{1}{m^{12} }$

Which statement explains Lauren's error

Answer:

• She should have multiplied the exponents instead of adding them

Step-by-step explanation:

The error in her workings is that she added the exponent instead of multiplying them

According to the law of indices

$(x^{a})^{b} = x^{ab}$

From the above illustration, it'll be observed that the exponents a and b were multiplied instead of adding or subtracting

Same thing is applicable to this expression in Lauren's case

She ought to multiply -7 and -5 to give 35 not adding them to give -12

The right solution to the expression is as follows:

$(m^{-7} )^{-5} = m^{(-7)(-5)}$

$(m^{-7} )^{-5} = m^{(-7*-5)}$

$(m^{-7} )^{-5} = m^{35}$