Exponents and Powers

What is the value of \( 2^4 \)

The value of \( 2^4 \) is \( 2 \times 2 \times 2 \times 2 = 16 \).

\( 5^0 \) is equal to:

Any non-zero number raised to the power of 0 is 1.

The value of \( 10^3 \) is:

The value of \( 10^3 \) is \( 10 \times 10 \times 10 = 1000 \).

Which of the following is equal to \( 3^2 \)

The value of \( 3^2 \) is \( 3 \times 3 = 9 \).

\( 2^3 \times 2^2 = \)?

When multiplying exponents with the same base, you add the exponents: \( 2^3 \times 2^2 = 2^{3+2} = 2^5 \).

\( (3^2)^3 = \)?

When raising a power to another power, you multiply the exponents: \( (3^2)^3 = 3^{2 \times 3} = 3^6 \).

What is the value of \( 4^{-1} \)

A negative exponent means taking the reciprocal: \( 4^{-1} = \frac{1}{4} \).

\( x^5 \div x^2 = \)?

When dividing exponents with the same base, you subtract the exponents: \( x^5 \div x^2 = x^{5-2} = x^3 \).

Which of the following is equivalent to 81

81 is equivalent to \( 3^4 \) because \( 3 \times 3 \times 3 \times 3 = 81 \).

What is the reciprocal of \( 2^3 \)

The reciprocal of \( 2^3 = 8 \) is \( \frac{1}{8} \).

\( a^0 + b^0 = \)?

Any non-zero number raised to the power of 0 is 1, so \( a^0 + b^0 = 1 + 1 = 2 \).

If \( x = 2 \), what is the value of \( x^3 + x^2 \)

If \( x = 2 \), then \( x^3 + x^2 = 2^3 + 2^2 = 8 + 4 = 12 \).

Simplify: \( 5^2 \div 5 = \)

\( 5^2 \div 5 = 25 \div 5 = 5 \).

Which one is NOT a power of 2

18 is not a power of 2. The powers of 2 are 2, 4, 8, 16, 32, etc.

\( 9^0 + 10^0 = \)?

Any non-zero number raised to the power of 0 is 1, so \( 9^0 + 10^0 = 1 + 1 = 2 \).

If \( 2^x = 8 \), then \( x = \)?

Since \( 2^3 = 8 \), the value of \( x \) is 3.

The expression \( (2^3)^2 \) equals:

When raising a power to another power, you multiply the exponents: \( (2^3)^2 = 2^{3 \times 2} = 2^6 \).

Which of the following equals 100

100 is equal to \( 10^2 \).

What is the square of \( 3^2 \)

The square of \( 3^2 \) is \( (3^2)^2 = 3^4 = 81 \).

\( 7^1 \times 7^2 = \)?

When multiplying exponents with the same base, you add the exponents: \( 7^1 \times 7^2 = 7^{1+2} = 7^3 \).

\( (a^3)^2 = \)?

When raising a power to another power, you multiply the exponents: \( (a^3)^2 = a^{3 \times 2} = a^6 \).

Simplify: \( 10^4 \div 10^2 \)

When dividing exponents with the same base, you subtract the exponents: \( 10^4 \div 10^2 = 10^{4-2} = 10^2 \).

\( 2^5 = \)?

The value of \( 2^5 \) is \( 2 \times 2 \times 2 \times 2 \times 2 = 32 \).

Which is correct for the zero exponent rule?

The zero exponent rule states that any non-zero number raised to the power of 0 is 1.

\( x^{-2} = \)?

A negative exponent means taking the reciprocal: \( x^{-2} = \frac{1}{x^2} \).

Which one is equal to 16

Both \( 2^4 \) and \( 4^2 \) equal 16.

\( (x^4 y^2)^2 = \)?

When raising a product to a power, you raise each factor to that power: \( (x^4 y^2)^2 = x^{4 \times 2} y^{2 \times 2} = x^8 y^4 \).

\( 10^0 = \)?