If a exponent is within parentheses and than one on the outside, how do I simplify it ?

Question

(5^2)^3 in an equation similar to this, how would I simplify it ?

Answer 1

you already have some good answers. I would like to rephrase your question as follows (compare to your original):

If an exponential is within parentheses and then there's another exponent on the outside, how do I simplify it?

 

Your algebra textbook undoubtedly illustrates various applicable laws or properties. This one is often called a power of a power. It's extremely easy to recall, because if you look up at the exponents, you see two successive exponents separated by a right parenthesis--a cue to multiply those two exponents.

 

See Arturo's first equation in his response to you. Memorize this along with a^xa^y = a^x+y

 

Answer 2

Hi Andrea,

When you raise a power to a power, you multiply exponents in order to simplify the expression.

For example, if you have (a^3)^4, the expression is equal to a^12.

 

Notice that (a^3)^4 = (a^3)(a^3)(a^3)(a^3) = a^(3+3+3+3) = a^12

 

So, the problem you offered, (5^2)^3 would equal 5^6.

 

Hope this helps.

 

 

 

Answer 3

You can use the power raised to a power rule. Basically, you multiply the exponents and keep the base value.

 

(x^m)ⁿ = x^mn

 

 

Therefore,

 

(5²)³ = 5⁶

Answer 4

The rule is

 

(a^x)^y = a^xy

 

(5²)³ = 5⁽²⁾⁽³⁾ = 5⁶