# Answer to Question #21517 in Algebra for Abby

Question #21517

How do you multiply exponents?

Expert's answer

You can multiply many exponential expressions together without having to change their form into the big or small numbers they represent. When multiplying exponents, the only requirement is that the bases of the exponential expressions have to be the same. So, you can multiply

2^4·2^6, a^6·a^8,

but you can't multiply

3^5·4^5

because the bases are not the same (although the exponents are).

To multiply powers of the same base, add the exponents together:

x^a·x^b = x^(a+b).

So,

2^4·2^9 = 2^(4+9) = 2^13.

If there’s more than one base in an expression with powers, you can combine the numbers with the same bases, find the values, and then write them all together. For example,

3^2·2^2·3^3·2^4 = 3(2+3)·2^(2+4) = 3^5·2^6.

Here's an example with a number that has no exponent showing:

4x^6y^5x^4y^1 = 4x^(6+4)y^(5+1) = 4x^10y^6.

When there’s no exponent showing, such as with y, you assume that the exponent is 1, so in the above example, you write y^1.

2^4·2^6, a^6·a^8,

but you can't multiply

3^5·4^5

because the bases are not the same (although the exponents are).

To multiply powers of the same base, add the exponents together:

x^a·x^b = x^(a+b).

So,

2^4·2^9 = 2^(4+9) = 2^13.

If there’s more than one base in an expression with powers, you can combine the numbers with the same bases, find the values, and then write them all together. For example,

3^2·2^2·3^3·2^4 = 3(2+3)·2^(2+4) = 3^5·2^6.

Here's an example with a number that has no exponent showing:

4x^6y^5x^4y^1 = 4x^(6+4)y^(5+1) = 4x^10y^6.

When there’s no exponent showing, such as with y, you assume that the exponent is 1, so in the above example, you write y^1.

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