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) = (1)/(m^(12) )`

Which statement explains Lauren's error

Answer:

• She should have multiplied the exponents instead of adding them

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)`