# ISEE Upper Level Math : How to multiply exponents

## Example Questions

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### Example Question #1 : How To Multiply Exponents

Explanation:

Subtract the numbers inside the parentheses first.  This leaves you with 3, which you then raise to the 3rd power:

### Example Question #1 : How To Multiply Exponents

Evaluate:

The expression is undefined.

Explanation:

Any nonzero number taken to the power of 0 is equal to 1, so

### Example Question #2 : How To Multiply Exponents

Multiply:

Explanation:

Use the FOIL method:

### Example Question #1 : How To Multiply Exponents

Evaluate:

Explanation:

Based on the power rule for exponents we can write:

That means; to raise a power to a power we need to multiply the exponents. In addition, based on the product rule for exponents in order to multiply two exponential terms with the same base, we need to add their exponents:

So we can write:

### Example Question #13 : Exponents

Simplify:

Explanation:

Based on the product rule for exponents in order to multiply two exponential terms with the same base, add their exponents:

So we can write:

### Example Question #2 : How To Multiply Exponents

Evaluate:

Explanation:

Based on the power rule for exponents we can write:

That means; to raise a power to a power we need to multiply the exponents. In addition, based on the product rule for exponents, in order to multiply two exponential terms with the same base we need to add their exponents:

So we can write:

in order to divide two exponents with the same base, we can keep the base and subtract the powers. So we get:

### Example Question #3 : How To Multiply Exponents

Evaluate:

Explanation:

Based on the negative exponent rule we have:

which says negative exponents in the numerator get moved to the denominator and become positive exponents. And negative exponents in the denominator get moved to the numerator and become positive exponents. So we can write:

In addition, based on the power rule for exponents we can write:

That means; to raise a power to a power we need to multiply the exponents. We also know that when a fraction is raised to a power, the numerator and the denominator are both raised to that power. So we can write:

### Example Question #1 : How To Multiply Exponents

If , find the value of:

Explanation:

Based on the power rule for exponents we can write:

That means; to raise a power to a power we need to multiply the exponents. So we can write:

Substitute and we get:

### Example Question #1 : How To Multiply Exponents

Simplify:

Explanation:

Based on the power rule, we know that in order to raise a power to a power we need to multiply the exponents, i.e.

.

Simplify: