# ACT Aspire Math: Taking Shortcuts with Exponent Properties

What is the value of (-2)⁶?

ACT Aspire | Math |

ACT Aspire Math | Expressions & Equations |

Math | Expressions & Equations |

Product Type | ACT Aspire |

Test Prep | ACT Aspire ACT Aspire Math |

### Transcript

times But well that's not terribly efficiently Not all the

time Instead we can use the properties of exponents to

take a shortcut Well the power rule for exponents tells

us that when one term with exponents is raised to

another exponents weaken simplify the expression by multiplying the two

exponents In other words x to the a power that

quantity to the b is the same as x to

the quantity eight times be so we can use this

route change the problem so that we can work with

a familiar cube root and square root Familiar like we

know two squared for without really been thinking about it

Right So what does that give us Let's factor out

something's here we got negative two to the six that

quantity which is the same as negative too toothy three

times two which is the same as a double quantity

thing here negative two cubed and then square so if

we do all that out that gets us negative eight

squared right because two four eight would be to cuba

And then we've got negative to cube being negative eight

and negative Eight square to sixty four so negative to

to the sixth power is positive sixty four and negative

sixty four's and b might be tempting but it's incorrect

because any imager raised two and even power must be

a positive number So anyway that's it It's sixteen And

yes you could have brute force this one just as

easily But we're doing this says that the on the

exam when they give you to the seventeenth power in

the thirty fourth power you can kind of do it 00:01:42.163 --> [endTime] quicker and easier Hopefully good luck with that