The Product Rule of Exponents states that when multiplying two numbers with the same base, you can add their exponents.
In this case, we have 6^8 * 6^3. Since both numbers have the same base of 6, we can add their exponents: 8 + 3 = 11.
Therefore, the simplified expression is 6^11.
The answer is B. 6^11.
Use the Product Ruled of Exponents to simplify 6^8 × 6^3.
A. 36^24
B. 6^11
C. 6^24
D. 36^11
5 answers
Find the numerical equivalent of 8^9 × 8^-5.
A. 0.002
B. 32,768
C. 512
D. 4,096
A. 0.002
B. 32,768
C. 512
D. 4,096
The Numerical Equivalent of a power is obtained by evaluating the base raised to the exponent.
In this case, we have 8^9 * 8^-5.
When multiplying powers with the same base, we add their exponents. In this case, 9 + (-5) = 4.
Therefore, the simplified expression is 8^4.
To find the numerical equivalent of 8^4, we calculate 8 * 8 * 8 * 8, which is equal to 4,096.
Therefore, the numerical equivalent of 8^9 * 8^-5 is 4,096.
The answer is D. 4,096.
In this case, we have 8^9 * 8^-5.
When multiplying powers with the same base, we add their exponents. In this case, 9 + (-5) = 4.
Therefore, the simplified expression is 8^4.
To find the numerical equivalent of 8^4, we calculate 8 * 8 * 8 * 8, which is equal to 4,096.
Therefore, the numerical equivalent of 8^9 * 8^-5 is 4,096.
The answer is D. 4,096.
What is the missing exponent in the following equation? n^365/n^? = n^152
A. n^213
B. n^517
C. n^2.4
D. n^55480
A. n^213
B. n^517
C. n^2.4
D. n^55480
To find the missing exponent, we can use the quotient rule of exponents, which states that when dividing two numbers with the same base, we subtract their exponents.
In this case, we have n^365/n^? = n^152.
Using the quotient rule, we can subtract the exponents: 365 - ? = 152.
To isolate the missing exponent, ? in this case, we can subtract 152 from both sides of the equation: 365 - 152 = ?.
This simplifies to ? = 213.
Therefore, the missing exponent in the equation is n^213.
The answer is A. n^213.
In this case, we have n^365/n^? = n^152.
Using the quotient rule, we can subtract the exponents: 365 - ? = 152.
To isolate the missing exponent, ? in this case, we can subtract 152 from both sides of the equation: 365 - 152 = ?.
This simplifies to ? = 213.
Therefore, the missing exponent in the equation is n^213.
The answer is A. n^213.