Multiplying Powers with the Same Base

Front

What is the product of powers with the same base?

Back

When multiplying powers with the same base, you add the exponents. For example, a^m * a^n = a^(m+n).

Front

How do you simplify the expression (2a^2b^4z)(6a^3b^2z^5)?

Back

You multiply the coefficients (2*6=12) and add the exponents for like bases: a^(2+3)=a^5, b^(4+2)=b^6, z^(1+5)=z^6. The simplified expression is 12a^5b^6z^6.

Front

What is the result of simplifying (8yz)(-8y^2z^3)?

Back

Multiply the coefficients (8*-8=-64) and add the exponents for like bases: y^(1+2)=y^3, z^(1+3)=z^4. The result is -64y^3z^4.

Front

How do you simplify the expression (-5b^3)(-3b^6)?

Back

Multiply the coefficients (-5*-3=15) and add the exponents for like bases: b^(3+6)=b^9. The simplified expression is 15b^9.

Front

What is the simplified form of x multiplied by itself six times?

Back

x * x * x * x * x * x = x^6.

Front

How do you rewrite the expression (2^4)(2^5) as a power?

Back

When multiplying powers with the same base, add the exponents: 2^(4+5) = 2^9.

Front

What is the rule for multiplying powers with different bases?

Back

When multiplying powers with different bases, you cannot combine the exponents. For example, a^m * b^n remains as is.

Front

What happens when you multiply a power by one?

Back

Any power multiplied by one remains unchanged: a^m * 1 = a^m.

Front

What is the result of (x^3)(x^2)?

Back

When multiplying powers with the same base, add the exponents: x^(3+2) = x^5.

Front

How do you simplify (3x^2)(4x^3)?

Back

Multiply the coefficients (3*4=12) and add the exponents for like bases: x^(2+3)=x^5. The result is 12x^5.