Exponents

Front

What is the power of a product rule in exponents?

Back

When multiplying two expressions with the same base, you add the exponents: a^m * a^n = a^(m+n).

Front

What is the power of a power rule in exponents?

Back

When raising a power to another power, you multiply the exponents: (a^m)^n = a^(m*n).

Front

What is the power of a quotient rule in exponents?

Back

When dividing two expressions with the same base, you subtract the exponents: a^m / a^n = a^(m-n).

Front

What is the zero exponent rule?

Back

Any non-zero base raised to the power of zero equals one: a^0 = 1 (where a ≠ 0).

Front

What is the negative exponent rule?

Back

A negative exponent indicates the reciprocal of the base raised to the opposite positive exponent: a^(-n) = 1/(a^n) (where a ≠ 0).

Front

How do you simplify (6x^7)^2?

Back

You apply the power of a power rule: (6^2)(x^(7*2)) = 36x^14.

Front

How do you simplify (2^4)(2^5)?

Back

You apply the power of a product rule: 2^(4+5) = 2^9.

Front

What is the result of simplifying x^12/y^22?

Back

This expression is already simplified; it represents the division of x raised to the 12th power by y raised to the 22nd power.

Front

How do you simplify (ab^8c)(a^-17c^10)?

Back

You combine like bases: a^(1-17)b^8c^(1+10) = (b^8c^11)/(a^16).

Front

What is the definition of an exponent?

Back

An exponent indicates how many times a number (the base) is multiplied by itself.