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If b^(3)*(b^(4))^(2)=b^(x), what is the value of x ? Choose 1 answer: (A) 9 (B) 11 (C) 18 (D) 19

If b3⋅(b4)2=bx b^{3} \cdot\left(b^{4}\right)^{2}=b^{x} , what is the value of x x ?\newlineChoose 11 answer:\newline(A) 99\newline(B) 1111\newline(C) 1818\newline(D) 1919

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Full solution

Q. If b3⋅(b4)2=bx b^{3} \cdot\left(b^{4}\right)^{2}=b^{x} , what is the value of x x ?\newlineChoose 11 answer:\newline(A) 99\newline(B) 1111\newline(C) 1818\newline(D) 1919
  1. Simplify using properties of exponents: We need to simplify the left side of the equation using the properties of exponents. The property (bm)n=bm∗n(b^{m})^{n} = b^{m*n} allows us to simplify (b4)2(b^{4})^{2}.
  2. Apply property to simplify: Using the property, we get (b4)2=b4×2=b8(b^{4})^{2} = b^{4\times2} = b^{8}.
  3. Combine exponents: Now we have b3∗b8b^{3} * b^{8}. Using the property of exponents that states bm∗bn=bm+nb^{m} * b^{n} = b^{m+n}, we can combine the exponents.
  4. Apply equality of exponents: Combining the exponents, we get b(3+8)=b11b^{(3+8)} = b^{11}.
  5. Determine the value of xx: Now we have the equation b11=bxb^{11} = b^{x}. Since the bases are the same and the equation is an equality, the exponents must be equal.
  6. Determine the value of xx: Now we have the equation b11=bxb^{11} = b^{x}. Since the bases are the same and the equation is an equality, the exponents must be equal.Therefore, xx must be equal to 1111.

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