Question

4 raised to x + 6 raised to x = g raised to x

Answer 1

Step-by-step explanation:

There are two specially-named powers: "to the second power" is generally pronounced as "squared", and "to the third power" is generally pronounced as "cubed". So "53" is commonly pronounced as "five cubed".

When we deal with numbers, we usually just simplify; we'd rather deal with "27" than with "33". But with variables, we need the exponents, because we'd rather deal with "x6" than with "x‍x‍x‍x‍x‍x".

Exponents have a few rules that we can use for simplifying expressions.

Simplify (x3)(x4).

To simplify this, I can think in terms of what those exponents mean. "To the third" means "multiplying three copies" and "to the fourth" means "multiplying four copies". Using this fact, I can "expand" the two factors, and then work backwards to the simplified form. First, I expand:

(x3)(x4) = (x‍x‍x)(x‍x‍x‍x)

Now I can remove the parentheses and put all the factors together:

(x‍x‍x)(x‍x‍x‍x) = x‍x‍x‍x‍x‍x‍x

This is seven copies of the variable. "Multiplying seven copies" means "to the seventh power", so this can be restated as:

x‍x‍x‍x‍x‍x‍x = x7

Putting it all together, the steps are as follows:

(x3)(x4) = (x‍x‍x)(x‍x‍x‍x)

= x‍x‍x‍x‍x‍x‍x

= x7

Then the simplified form of (x3)(x4) is:

x7

Note that x7 also equals x(3+4). This demonstrates the first basic exponent rule:

Whenever you multiply two terms with the same base, you can add the exponents:

( x m ) ( x n ) = x( m + n )

However, we can NOT simplify (x4)(y3), because the bases are different: (x4)(y3) = x‍x‍x‍xyyy = (x4)(y3). Nothing combines.

Simplify (a5 b3) (a b7).

Now that I know the rule (namely, that I can add the powers on the same base), I can start by moving the bases around to get all the same bases next to each other:

(a5 b3) (a b7) = (a5) (a) (b3) (b7)

Affiliate