Why does hot air rise from pavement on a hot summer day?(1 point)
Responses
Due to convection
Due to convection
Due to insulation
Due to insulation
Due to conduction
Due to conduction
Due to radiation
Due to convection
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Can you apply the Properties of Integer Exponents to generate equivalent expressions to 2 to the power of 2/2 to the power of −4
with only positive exponents, then solve the expression? Provide the solution as a whole number.
Certainly! Let's start by applying the properties of integer exponents to rewrite 2^(2/2) ÷ 2^(-4) with only positive exponents.
First, let's simplify 2^(2/2). The exponent 2/2 simplifies to 1, so we have 2^1.
Next, let's apply the exponent rule for division, which states that a^m ÷ a^n = a^(m-n). In this case, we have 2^1 ÷ 2^(-4).
Applying the exponent rule, we subtract the exponents: 1 - (-4) = 1 + 4 = 5.
So, 2^(2/2) ÷ 2^(-4) becomes 2^5.
Now, let's solve the expression 2^5 to a whole number:
2^5 = 2 × 2 × 2 × 2 × 2 = 32.
Therefore, the solution to the expression 2^(2/2) ÷ 2^(-4), with only positive exponents, is 32.
I hope this helps! Let me know if you have any further questions.
Apply the Properties of Integer Exponents to generate equivalent expressions to 4 to the power of 0 ⋅ 5 to the power of −2/(−2) to the power of −3 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents
Sure! Let's apply the properties of integer exponents to simplify the expression and rewrite it with only positive exponents.
First, let's simplify 4^0. Any number (except zero) raised to the power of 0 is equal to 1. So, 4^0 = 1.
Next, let's simplify 5^(-2). The negative exponent indicates that we take the reciprocal of the base raised to the positive exponent. So, 5^(-2) = 1/(5^2) = 1/25.
Now, let's simplify (-2)^(-3). Similar to the previous step, the negative exponent indicates that we take the reciprocal of the base raised to the positive exponent. So, (-2)^(-3) = 1/((-2)^3) = 1/(-8) = -1/8.
Now we can rewrite the expression: 4^0 ⋅ 5^(-2)/((-2)^(-3))
Using the properties of exponents for multiplication and division, we have:
4^0 ⋅ (1/25)/(-1/8)
Since any number (except zero) raised to 0 is 1, we can simplify further:
1 ⋅ (1/25)/(-1/8)
Multiplying by the reciprocal of a fraction is equivalent to dividing, so we can rewrite:
(1/25) ÷ (-1/8)
Dividing by a fraction is the same as multiplying by its reciprocal, so we can rewrite:
(1/25) × (-8/1)
Now, multiplying fractions is simply multiplying the numerators and denominators:
1 × (-8) = -8
25 × 1 = 25
Therefore, the simplified fraction with no remaining exponents is -8/25.
So, the solution to the expression 4^0 ⋅ 5^(-2)/((-2)^(-3)), with only positive exponents, is -8/25.
I hope this clarifies the solution for you! Let me know if you have any further questions.