1) 3^7 can be written as (3^4) * (3^3)
2) 3^7 can also be written as (3^6) * 3
What are 2 different way to write 3^7 as the product of two powers
3 answers
Explain why both of the expressions are equal to 3^7
Both of the expressions are equal to 3^7 because multiplication of powers follows the rule that when multiplying powers with the same base, you add the exponents.
In the first expression, (3^4) * (3^3), the base 3 is the same in both terms. Adding the exponents gives us 4 + 3 = 7, so the expression simplifies to 3^7.
In the second expression, (3^6) * 3, again we have the same base 3. The exponent 6 multiplied by 1 is 6, so the expression simplifies to 3^7.
In the first expression, (3^4) * (3^3), the base 3 is the same in both terms. Adding the exponents gives us 4 + 3 = 7, so the expression simplifies to 3^7.
In the second expression, (3^6) * 3, again we have the same base 3. The exponent 6 multiplied by 1 is 6, so the expression simplifies to 3^7.
1 answer