Write the expression using a single exponent.

2^2 * 2^8

A. 4^10
B. 2^10
C. 4^16
D. 2^16

Write the expression using scientific notation.

(2.5 * 10^4)(4 * 10^3

A. 10 * 10^7
B. 10 * 10^8
C. 1 * 10^8
D. 10 * 10^12

To be clear:

2^2 + 2^8
B. 2^10

(2.5 * 10^4)(4 * 10^3)
C. 1 * 10^8

A. 4^10

B. 2^10
C. 4^16
D. 2^16

Well, if we have 2^2 * 2^8, we can combine the two exponents because we're multiplying the same base, which is 2.

So 2^2 * 2^8 becomes 2^(2+8), which is equal to 2^10.

So the answer is B. 2^10.

Now, let's move on to the second question!

A. 10 * 10^7
B. 10 * 10^8
C. 1 * 10^8
D. 10 * 10^12

We have (2.5 * 10^4)(4 * 10^3).

To express this in scientific notation, we need to multiply the two numbers and then adjust the exponent accordingly.

So (2.5 * 10^4)(4 * 10^3) becomes 10 * (2.5 * 4) * (10^4 * 10^3), which simplifies to 10 * 10 * (2.5 * 4) * (10^7).

Now, let's consider the numbers alone. 10 * 10 is 100, and 2.5 * 4 is 10.

So we have 100 * 10 * (10^7), which is equal to 10 * 10^7.

Therefore, the answer is A. 10 * 10^7.

I hope that brings a smile to your face!

To write the expression 2^2 * 2^8 using a single exponent, you can apply the rule for multiplying powers with the same base. The rule states that when you multiply two powers with the same base, you add their exponents.

So, applying this rule, we have:

2^2 * 2^8 = 2^(2+8) = 2^10

Therefore, the expression can be written as 2^10. The correct answer is B.

To write the expression (2.5 * 10^4)(4 * 10^3) using scientific notation, you can multiply the coefficients and add the exponents of 10.

So, applying this rule, we have:

(2.5 * 10^4)(4 * 10^3) = (2.5 * 4) * (10^4 * 10^3) = 10 * 10^(4+3) = 10 * 10^7

Therefore, the expression can be written as 10 * 10^7. The correct answer is A.

Bosnian is right guys-

x ^ a * x ^ b = x ^ ( a + b )

2 ^ 2 * 2 ^ 8 = 2 ^ ( 2 + 8 ) = 2 ^ 10

( 2.5 * 10 ^ 4 )( 4 * 10 ^ 3 ) = 2.5 * 4 * 10 ^ ( 4 + 3 ) = 10 * 10 ^ 7 = 10 ^ 1 * 10 ^ 7 = 10 ^ ( 1 + 7 ) = 10 ^ 8