Correct Question
Lauren simplified the expression
![(m^{-7} )^{-5}](/tpl/images/0644/0237/02309.png)
as shown
![(m^{-7} )^{-5} = m^{-7+(-5)} = m^{-12} = \frac{1}{m^{12} }](/tpl/images/0644/0237/45ab7.png)
Which statement explains Lauren's error
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}](/tpl/images/0644/0237/baf58.png)
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)}](/tpl/images/0644/0237/47994.png)
![(m^{-7} )^{-5} = m^{(-7*-5)}](/tpl/images/0644/0237/85c0c.png)
![(m^{-7} )^{-5} = m^{35}](/tpl/images/0644/0237/7eafd.png)