How do you simplify #(2xy^6)^5#?

Answer 1

The answer will be #32x^5y^30#. Explanation follows...

When you make a power in which the base is another power, the simplifying involves multiplying the exponents. For example

#(x^3)^4= x^(3*4)=x^12#

Here's why:

#x^3 = x*x*x#

so, #(x^3)^4=(x*x*x)*(x*x*x)*(x*x*x)*(x*x*x)#

which, as you can see is nothing more than twelve #x#'s all multiplied in one product, and that can be written #x^12#.

Don't forget that is you see no exponent on a base, you are to imagine a #1# there.

So #(2xy^6)^5=2^5*x^5*(y^6)^5=32x^5y^30#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Avery Alexander

To simplify ( (2xy^6)^5 ), you apply the power of a power property, which states that to raise a power to another power, you multiply the exponents.

[ (2xy^6)^5 = 2^5 \cdot x^5 \cdot (y^6)^5 ]

[ = 32 \cdot x^5 \cdot y^{6 \times 5} ]

[ = 32x^5y^{30} ]

So, ( (2xy^6)^5 ) simplifies to ( 32x^5y^{30} ).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.