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.

.

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:

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:

Simplify the following:

Let's begin by recalling two rules

1. When multiplying variables with a common base, add the exponents.

2. When multiplying variables with a common base, multiply the coefficients.

So, our answer is

When exponents are multiplied by each other, the powers should be added together. Meanwhile, numbers not raised to an exponent are simply multiplied by each other.

Therefore, the answer is , because , and .

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:

When an exponent is raised to another exponent, the exponents should be multiplied toghether. This will result in:

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:

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

The Negative Exponent Rule says .

The power rule says that, in order to raise a power to a power, we need to multiply the exponents, i.e. .