Question

match the expression with its simplified form using multiplication law
$6k^3$ $6k^2 \cdot k$ $2^5$ $3^4$
$12x^3$ $2n^4 \cdot 5n^4$ $40b^3$ $10n^8$
$2 \cdot 2^2 \cdot 2^2$ $12n^8$ $4x^2 \cdot 3x$ $3^2 \cdot 3^2$
$2n^4 \cdot 6n^4$ $6x \cdot 6x^3$ $36x^4$ $5b^2 \cdot 8b$

Explanation:

Step1: Recall the Multiplication Law of Exponents

The multiplication law for exponents states that \(a^m \cdot a^n = a^{m + n}\) when multiplying terms with the same base. Also, for coefficients, we multiply them as regular numbers.

Step2: Analyze each pair

• For \(6k^2 \cdot k\):

Using the exponent law, \(k^2 \cdot k = k^{2 + 1}=k^3\), and the coefficient is \(6\), so \(6k^2 \cdot k = 6k^3\).

• For \(2n^4 \cdot 5n^4\):

Coefficients: \(2\times5 = 10\), exponents: \(n^4 \cdot n^4=n^{4 + 4}=n^8\), so \(2n^4 \cdot 5n^4 = 10n^8\).

• For \(2\cdot2^2\cdot2^2\):

Using the exponent law, \(2^1\cdot2^2\cdot2^2=2^{1 + 2+2}=2^5\).

• For \(4x^2 \cdot 3x\):

Coefficients: \(4\times3 = 12\), exponents: \(x^2 \cdot x=x^{2 + 1}=x^3\), so \(4x^2 \cdot 3x = 12x^3\).

• For \(3^2 \cdot 3^2\):

Using the exponent law, \(3^2 \cdot 3^2=3^{2+2}=3^4\).

• For \(2n^4 \cdot 6n^4\):

Coefficients: \(2\times6 = 12\), exponents: \(n^4 \cdot n^4=n^{4 + 4}=n^8\), so \(2n^4 \cdot 6n^4 = 12n^8\).

• For \(6x \cdot 6x^3\):

Coefficients: \(6\times6 = 36\), exponents: \(x \cdot x^3=x^{1+3}=x^4\), so \(6x \cdot 6x^3 = 36x^4\).

• For \(5b^2 \cdot 8b\):

Coefficients: \(5\times8 = 40\), exponents: \(b^2 \cdot b=b^{2 + 1}=b^3\), so \(5b^2 \cdot 8b = 40b^3\).

Answer:

The matches are:

• \(6k^2 \cdot k\) matches \(6k^3\)
• \(2n^4 \cdot 5n^4\) matches \(10n^8\)
• \(2\cdot2^2\cdot2^2\) matches \(2^5\)
• \(4x^2 \cdot 3x\) matches \(12x^3\)
• \(3^2 \cdot 3^2\) matches \(3^4\)
• \(2n^4 \cdot 6n^4\) matches \(12n^8\)
• \(6x \cdot 6x^3\) matches \(36x^4\)
• \(5b^2 \cdot 8b\) matches \(40b^3\)