Midterm Practice

Answer explanation

Simplify the following:

x² ⋅ x⁴ = x⁶

When multiplying exponents with the same base, keep the be and ADD the exponents

Answer explanation

Simplify the following:

3x² ⋅ 2x⁴ = 6x⁶

When multiplying exponents with the same base:

-Multiply the coefficients

-ADD the exponents

Answer explanation

Simplify the following:

(x³)⁴ = x¹²

This is power of power rule:

When taking an exponent to another power, keep the base and multiply the exponents.

Answer explanation

Simplify the following:

(5x⁵)² = 25x¹⁰

This is power of power rule:

When taking an exponent to another power:

-Coefficient gets the exponent (5^2 = 25)

-multiply the exponents.

• 1

Answer explanation

Simplify the following:

x⁵ ⋅ x^-5 = x^{5 + -5} = x⁰ = 1

Anything to the power of 0 equals 1

Answer explanation

Simplify the following:

(c⁵)(c³)(c³)

This is just the product rule, keep the base and ADD the exponents.

c⁵⁺³⁺³ = c¹¹

Answer explanation

Simplify the following:

(2x⁴y⁷)³

Remember the 3 belongs to everything

2³ x⁽⁴⁾⁽³⁾ y⁽⁷⁾⁽³⁾

8x¹²y²¹