Exponentiation with Integer Exponents

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What is an integer exponent?

An integer exponent indicates how many times a base number is multiplied by itself.

How do you express '5 to the power of 3' using exponents?

5^3, which means 5 multiplied by itself 3 times (5 × 5 × 5).

What is the result of multiplying any number by 0 as the exponent?

Any number raised to the power of 0 is 1.

How do you calculate 2^4?

2^4 is calculated as 2 × 2 × 2 × 2 = 16.

What is the value of (–3)^2?

The value is 9 because (–3) × (–3) = 9.

What does a negative exponent indicate?

A negative exponent indicates the reciprocal of the base raised to the opposite positive exponent.

How do you simplify 3^(-2)?

3^(-2) is simplified to 1/3^2, or 1/9.

What is 10^3 in standard form?

10^3 in standard form is 1000.

How do you compute (4^3)/(4^2)?

You subtract the exponents: 4^(3-2) = 4^1 = 4.

What is the product of (2^3) * (2^2)?

You add the exponents: 2^(3+2) = 2^5 = 32.

Explain 0^n, where n is any positive integer.

0^n equals 0 because 0 multiplied by itself any number of times is still 0.

How is a^(-n) expressed in terms of fractions?

a^(-n) is expressed as 1/a^n.

What is the simplified form of (x^3)^4?

(x^3)^4 is simplified to x^(3*4) = x^12.

If 5^0 = x, what is x?

x equals 1, because any number to the power of 0 is 1.

How do you explain the exponent rule for dividing powers with the same base?

Subtract the exponents: a^(m-n) when you divide a^m by a^n.